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In computer graphics, swizzles are a class of operations that transform vectors by rearranging components. [1] Swizzles can also project from a vector of one dimensionality to a vector of another dimensionality, such as taking a three-dimensional vector and creating a two-dimensional or five-dimensional vector using components from the original vector. [2]
In mathematics, for positive integers k and s, a vectorial addition chain is a sequence V of k-dimensional vectors of nonnegative integers v i for −k + 1 ≤ i ≤ s together with a sequence w, such that v −k+1 = [1,0,0,...0,0] v −k+2 = [0,1,0,...0,0] â‹® â‹® v 0 = [0,0,0,,...0,1] v i =v j +v r for all 1≤i≤s with -k+1≤j, r≤i-1 v s ...
A vector addition system (VAS) is one of several mathematical modeling languages for the description of distributed systems.Vector addition systems were introduced by Richard M. Karp and Raymond E. Miller in 1969, [1] and generalized to vector addition systems with states (VASS) by John E. Hopcroft and Jean-Jacques Pansiot in 1979. [2]
Basic Linear Algebra Subprograms (BLAS) is a specification that prescribes a set of low-level routines for performing common linear algebra operations such as vector addition, scalar multiplication, dot products, linear combinations, and matrix multiplication.
A vector space over a field F (often the field of the real numbers) is a set V equipped with two binary operations. Elements of V are called vectors, and elements of F are called scalars. The first operation, vector addition, takes any two vectors v and w and outputs a third vector v + w.
Vector addition and scalar multiplication: a vector v (blue) is added to another vector w (red, upper illustration). Below, w is stretched by a factor of 2, yielding the sum v + 2 w . In mathematics and physics , a vector space (also called a linear space ) is a set whose elements, often called vectors , can be added together and multiplied ...
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